Lemma 4.1 (Ashikhmin-Barg condition for p=2) [1]}
Let \(C\)  be a linear code over \(\mathbb {Z}_2\) . Denote \(w_0\)  as the minimum(nonzero) and \(w_{\infty }\)  as the maximum Hamming weights. If \(\frac{w_0}{w_{\infty }}>\frac{1}{2}\) , then \(C\)  is minimal.

